Representations of additive categories and direct-sum decompositions of objects Alberto Facchini 18E0516D70additive categoryKrull-Schmidt theoremcategorical equivalence The aim of this paper is to embed additive categories in which direct-sum decompositions into indecomposables are not unique but have a regular geometric behavior into categories in which the Krull-Schmidt Theorem holds, that is, to give a representation of additive categories into categories with unique direct-sum decompositions into indecomposables. Cf. Theorems 4.8, 6.1, 6.2, 7.2, and 8.2. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.2865 10.1512/iumj.2007.56.2865 en Indiana Univ. Math. J. 56 (2007) 659 - 680 state-of-the-art mathematics http://iumj.org/access/